CP620, Shock Compression of Condensed Matter - 2001
edited by M. D. Furnish, N. N. Thadhani, and Y. Horie
© 2002 American Institute of Physics 0-7354-0068-7/02/$ 19.00
SHOCK-INDUCED STRUCTURAL PHASE
TRANSFORMATIONS STUDIED BY
LARGE-SCALE MOLECULAR-DYNAMICS SIMULATIONS
Kai Kadau, Timothy C. Germaim, Peter S. Lomdahl, and Brad Lee Holian
Los Alamos National Laboratory, Los Alamos, NM 87545
Abstract Shock waves in martensitic Fe (bcc) induce a complex relaxation mechanism behind the shock front. Non-equilibrium multimillion-atom molecular-dynamics simulations
demonstrate that for shock strengths above the threshold for plastic deformation, small grains
of austenite (hep, fee) nucleate in the martensite matrix. The subsequent growth and orientation of the austenitic grains strongly depend on the crystallographic shock direction and
the shock strength. Crystallographic orientational relationships between the unshocked and
shocked material are quite similar to that found in the temperature-driven structural transformations (i.e. martensitic and austenitic transformations) in iron-based alloys. The influence
of the specific potential on the qualitative and the quantitative results of the simulations will
be discussed.
INTRODUCTION
Here we report on the first numerical simulations of
shock waves in martensitic Fe single crystals. As
observed experimentally, the relaxation of the shear
pressure behind the shock front is achieved by structural transformation from bcc to a closed packed
structure [1] rather than dislocation-induced plasticity as found in fee crystals [2, 3]. As for shock
waves in fee single crystals [3], the structure of the
shock front depends on the crystallographic shock
direction.
Molecular-dynamics (MD) simulations with
about 8 million atoms in the computational-cell
(i.e. 40.2nm x 40.2iim x 57.4nm) were performed with the high-performance code SPaSM
(Scalable Parallel Short-range Molecular-dynamics)
[4]. Shock waves along [OOljbcc and [110]bcc with
different shock-strength were initiated by a momentum mirror which specularly reflects any atom
reaching the mirror [2] using periodic boundary
conditions in the two transverse directions. The
forces between the atoms were calculated within the
embedded-atom method (EAM) including a pair interaction <I> as well as a density dependent term F:
(1)
whereby the summation is over all atoms and r^is the distance between the atoms i and j. The
function F(pi) represents the embedding energy of
atom i depending on the background charge density
which is the sum of the atomic contributions pat
(2)
In this work we used two different forms for the
EAM, namely the Daw and Baskes form [5] and
the potential proposed by Harrison, Voter, and
Chen [6]. The results shown in the next section
were performed with the potential developed by
Meyer and Entel [7] within the Daw and Baskes
ansatz. This potential was designed to study the
temperature-driven structural transition from bcc to
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moving faster than the following plastic front, converting to an overdriven plastic wave for very high
shock strength. An interesting feature is the possibility of over-relaxation of the shear stress for waves
along [OOljbcc (Fig. 2): The (001)bcc planes with an
ideal distance of 0.144 nm (the T = P = 0 cubic
lattice constant for Fe is 0.287 nm [7]) transform
fee and vice-versa in Fe and Fe-Ni alloys [8]. A
discussion about the differences of the results with
respect to the choice of potential is given at the end
of the report.
RESULTS
For low shock strengths, the single crystals only
uniaxially compress, which can be seen by the splitting and moving of the neighbor peaks of the radial distribution function with respect to the neighbor distances of the initial bcc structure (Fig. 1).
Above a critical shock strength the martensitic crystal transforms into an austenitic close-packed structure (Fig. 1).
Slightly above the transformation threshold,
shock waves in [001]bcc exhibit an elastic precursor
0.8
[001] SHOCK DIRECTION
0.6
>>
cc
0.4
I
0.2
1.75ps
3.5 ps
[001 ] shock direction _
—— [110] shock direction
V
i
• Ta
close-packed
0.2
0.3
0.4
T
T
T
0.5
r(nm)
Figure 1: Radial distribution function g(r) for different shocked bcc Fe single crystals. Weak shocks
only uniaxially compress the bcc which can be seen
in the splitting and moving of the peaks with respect
to the bcc peak positions. Shock waves above the
threshold for plastic deformation induce a structural
change from the bcc structure to a close-packed
structure (ideal fee and hep positions are marked
by circles and triangles, respectively). Maxima of
the radial distribution function of transformed Fe
due to shock waves in [011]bcc are broader due to
smaller austenite grains and thicker grain boundaries (Fig. 5).
-0.2
20
40
longitudinal position (nm)
Figure 2: Pressure- volume components for shock
waves well above the transformation threshold.
Whereas the austenitic transformation in shock
waves along [001]bcc direction can result to an
over-relaxation of the shear stress Pshear = P™ —
(Pxx + P yy )/2, the transformation from bcc to
close-packed for shock waves traveling along the
[110] bcc direction almost relaxes the anisotropy of
the pressure-tensor.
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both (lll)fcc planes with a distance of 0.209 nm,
and into (001)fcc planes (Fig. 4) with a distance
of 0.181 nm, thus facilitating the relaxation of the
anisotropy of the pressure-tensor (Fig. 2).
[001] SHOCK DIRECTION
fcc(HO)
bcc(001)
t[100]
Figure 3: The austenitic transition occurring for
shock waves traveling along the [OOljbcc direction
is due to a transformation from the (001)bcc plane
into the (110)fcc plane (shown) or into the equivalent (12lO)hcp plane (not shown).
into (llO)fcc planes (Fig. 3) with an ideal distance
of 0.128 nm (assuming same space filling for the
bcc and fee structure) which can result to an overrelaxation of the pressure component in the [001]
shock direction. Shocks along [110]bcc transform
the (llO)bcc planes with a distance of 0.203 nm into
[110] SHOCK DIRECTION
fCC(111)
bcc(HO)
[112]
fcc(001)
[110]
[010]
[100]
Figure 4: Shock waves moving along the [110]bcc
direction can transform the (llO)bcc plane into both
the (lll)fcc plane and the (001)fcc plane (or their
equivalent hep planes).
Figure 5: Cross-sections (40.2nm x 40.2nm) of
shocked samples showing the evolved austenitic
grains (light) separated by grain-boundaries (dark).
Shock waves along the [001]bcc direction (upper
panel) induce larger grains with thinner boundaries
than waves along [110]bcc direction (lower panel).
we are seeing realistic features of shock waves in
martensitic iron, even though the embedded-atom
approach neglets both magnetism and directional
bonding. Future work should take into account
these two features. Another future direction is the
systematic simulation of polycrystalline samples.
Numerous small austenitic grains start to nucleate
in the martensite matrix with subsequent growth of
the grains on a pico-second timescale. The resulting
austenitic polycrystal has a texture depending on the
shock direction due to the above described transformation mechanism. Shock waves in the [001]bcc direction induce larger grains with thinner boundaries
than shocks in [HOjbcc (Fig- 5). This might be due
to different energy barriers between the structures
for these crystallographic directions [9].
ACKNOWLEDGEMENTS
This work was carried out under the auspices
of the U.S. Dept. of Energy at LANL under contract W-7405-ENG-36. One of the authors (K. K.)
would like to thank P. Entel and the German Science
Council (DFG) (through SFB 445 and the Graduate
School Structure and Dynamics of Heterogeneous
Systems) for their support. Thanks to J. B. Maillet
for reading the manuscript.
INFLUENCE OF THE POTENTIAL
We found essentially identical qualitative results
for both potentials. The major difference is the
threshold pressure for the transformation from the
bcc structure into a close-packed structure. The
Meyer-Entel potential [7] was only fitted to zeropressure data (including the lattice constant, elastic
constants, zone-boundary phonon-frequencies, and
vacancy-formation energy) resulting in an excessively repulsive potential upon compression. Thus
the transition pressure of 55 GPa is much greater
than the experimental 13 GPa [10]. The potential from [6] approximately takes high pressure data
into account by incorporating a universal equationof-state (Rose function) [11] and therefore yields a
transformation pressure of about 15 GPa, which is
close to experimental observations.
REFERENCES
[I] Kadau, K., Germann, T.C., Lomdahl, P.S., and Holian, B.L., submitted to Science,
[2] Holian, B.L., and Lomdahl, P.S., Science 280, 2085
(1998); Holian, B.L., Phys. Rev. A 37,2562 (1988).
[3] Germann, T.C., Holian, B.L., Lomdahl, P.S., and
Ravelo, R., Phys. Rev. Lett. 84, 5351 (2000).
[4] Beazley, D.M., and Lomdahl, P.S., Par. Comput.
20, 173 (1994); Beazley, D.M., and Lomdahl, P.S.,
Comput. in Physics 11, 230 (1997).
[5] Daw, M.S., and Baskes, M.I., Phys. Rev. Lett. 50,
1285 (1983); Daw, M.S., and Baskes, M.I., Phys.
Rev. B 29, 6443 (1984).
SUMMARY AND CONCLUSIONS
Our work shows that the relaxation of the shear
stress behind shock fronts in polymorphic materials can be achieved by the structural transition from
one phase to another on a MD timescale (such transformations are of course well-known experimentally [10]) . In the special case of martensitic iron,
above a critical shock strength the transition from
bcc to a close-packed structure relaxes the shear
stress behind the shock front. We found that in
single crystals the structure of the shock front and
the growth of the austenitic grains evolving in the
martensitic matrix depend on the shock direction,
resulting in a highly textured polycrystal.
Simulations with different potentials for iron
show that the qualitative results depend not on the
specific potential, whereas quantitative data, such as
the pressure threshold for the transformation does.
This 'universal' behavior makes us confident that
[6] Harrison, R.J., Voter, A.F., and Chen, S.-P. in
Atomistic Simulation of Materials, Vitek, V., and
Srolovitz, D.J., Eds. (1989).
[7] Meyer, R., and Entel, P., Phys. Rev. B 57, 5140
(1998).
[8] Entel, P., Meyer, R., and Kadau, K., Philos. Mag.
B 80, 183 (2000); Kadau, K., Meyer, R., and Entel,
P., Surf. Rev. Lett. 6, 35 (1999).
[9] Kadau, K., Entel, P., Germann, T.C., Lomdahl, PS.,
and Holian, B.L., / Phys. 7V, in press (2001).
[10] Meyers, M.A., Dynamic Behavior of Materials,
Wiley-Interscience, New York, 1994; Duvall, G.E.
and Graham, R.A., Rev. Mod. Phys. 49, 523 (1974).
[II] Rose, J.H., Smith, J.R., Guinea, F., Ferrante, J.,
Phys. Rev. B 29, 2963 (1984).
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